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@shBang #!/usr/bin/env python3
@*
MMStepper.tmpl
Created by Damien Beard on 2013-08-07, with code adapted from Graham Dennis.
Last modified by Sean Wild on 2013-08-02.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*@
// Start of stepper
@extends xpdeint.Segments.Integrators._Stepper
@def name: MM
@attr $ipPropagationStepFractions = ['1']
@attr $nonconstantIPFields = 1
@attr $extraIntegrationArrayNames = ['akfield', 'aifield']
@attr $isCrossCapable = False
@attr $integrationOrder = 2.0
@*
Single integration step (MM)
*@
@def singleIntegrationStep($function)
@#
// Start of single step
@set $arguments = {'_step': '_step', $propagationDimension: $propagationDimension}
${transformVectorsToBasis($integrationVectors, $homeBasis)}@slurp
if (_istep == 0)
{
// a_k = a
${copyVectors($integrationVectors, '_akfield'), autoIndent=True}@slurp
// active vector = a_i
${assignVectorPointers($integrationVectors, '_active', '_aifield'), autoIndent=True}@slurp
// a_i = a
${copyVectors($integrationVectors, '_aifield'), autoIndent=True}@slurp
// a_i = G[a_i, t]
${callFunction('deltaA', arguments, parentFunction = function), autoIndent=True}
// transformToHomeSpace()
${transformVectorsToBasis($integrationVectors, $homeBasis), autoIndent=True}@slurp
// active vector = a
${assignVectorPointers($integrationVectors, '_active'), autoIndent=True}@slurp
// a = a + G[a_i, t]
${loopOverVectorsWithInnerContentTemplate($integrationVectors,
"""_${vector.id}[$index] += _aifield_${vector.id}[$index];
""", basis = $homeBasis), autoIndent=True}@slurp
${callFunction('nonconstantIPFields', arguments, _exponent = 1, _arrayIndex = 0, parentFunction = function), autoIndent=True}
// ipEvolve a +1
${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function), autoIdent=True}
// transformToHomeSpace()
${transformVectorsToBasis($integrationVectors, $homeBasis), autoIndent=True}@slurp
${propagationDimension} += _step;
} // For all steps past the first:
else
{
// active vector = a_k
${assignVectorPointers($integrationVectors, '_active', '_akfield'), autoIndent=True}@slurp
// ipEvolve a_k +1
${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function), autoIndent=True}
// transformToHomeSpace()
${transformVectorsToBasis($integrationVectors, $homeBasis), autoIndent=True}@slurp
// active vector = a_i
${assignVectorPointers($integrationVectors, '_active', '_aifield'), autoIndent=True}@slurp
// a_i = a
${copyVectors($integrationVectors, '_aifield'), autoIndent=True}@slurp
// a_i = G[a_i, t]
${callFunction('deltaA', arguments, parentFunction = function), autoIndent=True}
// transformToHomeSpace()
${transformVectorsToBasis($integrationVectors, $homeBasis), autoIndent=True}@slurp
// active vector = a_k
${assignVectorPointers($integrationVectors, '_active', '_akfield'), autoIndent=True}@slurp
// a_k = a_k + 2*a_i
${loopOverVectorsWithInnerContentTemplate($integrationVectors,
"""_akfield_${vector.id}[$index] = _akfield_${vector.id}[$index] + 2*_aifield_${vector.id}[$index];
""", basis = $homeBasis), autoIndent=True}@slurp
${callFunction('nonconstantIPFields', arguments, _exponent = 1, _arrayIndex = 0, parentFunction = function), autoIndent=True}
// ipEvolve a_k +1
${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function), autoIndent=True}
// transformToHomeSpace()
${transformVectorsToBasis($integrationVectors, $homeBasis), autoIndent=True}@slurp
// a = a_k, a_k = a
${swapVectorPointers($integrationVectors, '_akfield'), autoIndent=True}@slurp
${propagationDimension} += _step;
}
if (_istep == ($getVar('integrator.maxIntegrationStepsVar', $integrator.stepCount) - 1)) {
// active vector = a_k
${assignVectorPointers($integrationVectors, '_active', '_akfield'), autoIndent=True}@slurp
// ipEvolve a_k +1
${callFunction('ipEvolve', arguments, _exponent = +1, parentFunction = function), autoIndent=True}
// transformToHomeSpace()
${transformVectorsToBasis($integrationVectors, $homeBasis), autoIndent=True}@slurp
// active vector = a_i
${assignVectorPointers($integrationVectors, '_active', '_aifield'), autoIndent=True}@slurp
// a_i = a
${copyVectors($integrationVectors, '_aifield'), autoIndent=True}@slurp
// a_i = G[a_i, t]
${callFunction('deltaA', arguments, parentFunction = function), autoIndent=True}
// transformToHomeSpace()
${transformVectorsToBasis($integrationVectors, $homeBasis), autoIndent=True}@slurp
// a = 0.5*(a + a_k + G[a_i, t])
${loopOverVectorsWithInnerContentTemplate($integrationVectors,
"""_${vector.id}[$index] = 0.5*(_${vector.id}[$index] + _akfield_${vector.id}[$index] + _aifield_${vector.id}[$index]);
""", basis = $homeBasis), autoIndent=True}@slurp
if (($getVar('integrator.maxIntegrationStepsVar', $integrator.stepCount) % 2) == 0) {
// Odd number of vector swaps, need to swap back and memcpy
// so that the original vectors are deallocated correctly
${swapVectorPointers($integrationVectors, '_akfield'), autoIndent=True}@slurp
${copyVectors($integrationVectors, None, '_akfield'), autoIndent=True}@slurp
}
}
// To ensure correct sampling, set active dimension to vector
${assignVectorPointers($integrationVectors, '_active')}@slurp
// End of single step
@#
@end def
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